Publications of the Research Institute for Mathematical Sciences

On Algebraic #-Cones In Topological Tensor-Algebras, I Basic Properties and Normality

Gerald Hofmann[1]

(1) HTWK Leipzig, Germany

The concept of algebraic #-cones (alg-# cones) in topological tensor-algebras E⊗[τ] is introduced. It seems to be useful because the well-known cones such as the cone of positivity E⊗, the cone of reflection posilivity (Osterwalder-Schrader cone), and some cones of α-positivity in QFT with an indefinite metric are examples of alg-# cones.
It is investigated whether or not the known properties of E⊗ (e.g., E⊗ is a proper and generating cone not satisfying the decomposition property) apply to alg-# cones. For proving deeper results, the structure of the elements of alg-# cones is analyzed, and certain estimations between the homogeneous components of those elements are proven. Using them, a detailed investigation of the normality of alg-# cones is given.
Furthermore, the convex hull of finitely many alg-# cones is also considered.